On the physical origin of the fine-structure constant

¹ IES, Univ Montpellier, CNRS - 860 rue St Priest, F-34095 Montpellier cedex 5, France
² Department of Engineering, “Enzo Ferrari”, University of Modena and Reggio Emilia - Via P. Vivarelli, 10, I-41125 Modena, Italy
³ Mathematical and Physical Department, “Ennio De Giorgi”, Salento University - Via Monteroni, I-73100 Lecce, Italy

Received: 23 December 2025
Accepted: 29 January 2026

Abstract

The fine-structure constant α is a dimensionless constant introduced by sommerfeld in 1916. This number was interpreted as a way of quantifying the strength of the electromagnetic interaction. Since then, several physicists expressed their dissatisfaction waiting for a more direct interpretation. Here we propose a one-to-one correspondence between and the variance of the photon number inside a black-body of given volume and temperature. As a broader perspective we propose that any atomic spectral-line is associated with a line-structure constant that provides the macroscopic statistical information on the photon gas inside the corresponding black-body cubic cavity. From this point of view, the expression of the Sommerfeld constant is considered as a particular case that coincides exactly with our results when the black-body temperature corresponds to the equivalent temperature of the emission line of and with the cubic size of the black body .